The general statistical model assumed for the 1-way balanced
ANOVA problems is

where I denotes the number of treatments and
J denotes the number of replicates per treatment.

Methodology:

For all datasets, multiple precision calculations (accurate to 500 digits) were made
using the preprocessor and FORTRAN subroutine package of Bailey (1995, available from
NETLIB). Data were read
in exactly as multiple precision numbers and all calculations were made with this very
high precision. The results were output in multiple precision, and only then rounded
to fifteen significant digits. These multiple precision results are an
idealization. They represent what would be achieved if calculations were made without
roundoff or other errors. Any typical numerical algorithm (i.e. not implemented in
multiple precision) will introduce computational inaccuracies, and will produce results which differ
slightly from these certified values.

Definitions:

Within Treatment Sum of Squares

The certified values for the within treatment sum of squares
is defined by

Within Treatment Degrees of Freedom

The certified value of the within treatment degrees of freedom
is defined by

I(J - 1).

Within Treatment Mean Square

The certified value of the within treatment mean square is defined by

Between Treatment Sum of Squares

The certified values for the within treatment sum of squares
is defined by

Between Treatment Degrees of Freedom

The certified value of the within treatment degrees of freedom
is defined by

(I - 1).

Between Treatment Mean Square

The certified value of the between treatment mean square is defined by